temporal and spatial distribution of airspace complexity for air traffic controller workload-based...

7/26/2019 Temporal and Spatial Distribution of Airspace Complexity for Air Traffic Controller Workload-Based Sectorization

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American Institute of Aeronautics and Astronautics

1

Temporal and Spatial Distribution of Airspace Complexity

for Air Traffic Controller Workload-Based Sectorization

Arash Yousefi*and George L. Donohue

George Mason University, Fairfax, Virginia, 22030

We develop an Air Traffic Controller (ATC) workload-based methodology for airspace

sectorization. As an initial step, we partition the US National Airspace into three layers with

different altitude ranges. The range of each layer is based on the operational levels in low,

high, and ultra-high airspace. Each layer is further tiled to 2,566 hexagonal cells (hex-cells)

with 24 nautical mile sides. These hex-cells are assumed to be the finite elements of airspace

and ATC workload is modeled for each hex-cell using various airspace metrics. We simulate

a one-day scenario of the entire National Airspace System (NAS) and calculate the ATC

workload for each hex-cell. Furthermore, we apply new visualization techniques to analyze

the temporal and spatial distribution of the controller workload. Having the workload

values for each cell for the entire day, we develop clustering algorithms using optimization

theory to cluster cells and construct sectors. Our effort concentrates on simulation as ameans to evaluate cognitive workload for the elements of airspace regardless of current

sector and center boundaries.

Nomenclature

TotalWL = total ATC workload for a sector or group of sectors during a given time intervalWLHM = horizontal movement workload

WLCDR = conflict detection/resolution workload

WLC = coordination workloadWLAC = altitude-change workload

WLt = ATC workload function at time t

n = number of sectors

s = side of hex-cell in nautical milef = generic functiont = time index

lat = latitude in degree

lon = longitude in degree

I. Introduction

IR travel in the U.S. grew at a rapid pace until 2001, expanding from 172 million passenger enplanements in1970 to nearly 615 million in 2000. However, over the next 4 years, a combination of factorsthe events of

September 11th, 2001, an economic recession, and other factorscombined to reduce the traffic back to 1995 levels.

Never-the-less, air travel remains one of the most popular modes of transportation and it is projected to grow with a

rapid pace1. A combination of many factors limit the National Airspace System (NAS) capacity and it is expected

that current system capacity could not maintain a high quality of service for the future demand. The limited airspacecapacity is already imposing significant en route delay in the congested areas of the NAS1.

* Ph.D. Candidate and GRA, Center for Air Transportation Systems Research (CATSR), 4400 University Dr.,MSN4A6, AIAA Member.Professor and Director, Center for Air Transportation Systems Research (CATSR), 4400 University Dr., MSN4A6,

AIAA Member.

A


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A. Capacity limitations and the role of Air Traffic Controllers (ATCs)

The capacity of the nations air transportation system has not kept pace with the growth in demand. Thus costs in

terms of lost time and extra fuel consumed continue to grow rapidly for society and business2. Capacity of the NAS

is constrained by many factors including number of runways, aircraft separation requirements, and the Air Traffic

Controller (ATC) workload limitations. Future increasing demand could result in under utilization of the airspacesystem due to controller workload constraints. In congested areas of the NAS, the ATC workload limitation is a

critical capacity constraint which generates significant en route delay and increased Operational Errors (OE)5. The

controllers often enforce Miles in Trail (MIT) restrictions or they may reroute the aircraft or deny access into asector to avoid high workload situations. Without effective improvements to reduce the ATC workload in congested

areas, airspace capacity could not be maintained up to a level which satisfies the future growth.

Airspace sectorization has a direct impact on the amount of workload that controllers experience and an efficientsectorization could ease the workload even in the complex traffic situations3,4, and 6. The current airspace sectorization

is not based on a comprehensive and system-level study of demand profiles and route structures. The majority of

sector boundaries have a historical, not an analytical background3,4,7,& 19. Currently, modifications and airspace

redesigns are often conducted within Air Route Traffic Control Centers (ARTCC) and the system-wide effect of any

change to the entire NAS is not usually studied. Throughout the years sectors in the congested airspace have beendivided into smaller sectors to lower the aircraft density. However the available frequency spectrum for controller-

to-pilot and controller-to-controller communication eliminates the achievable number of sectors in the NAS8.

The ATC workload is directly related to the controllers situational awareness9. Structured air traffic reduces thesystem dynamics and enables the ATC to develop mental abstractions to reduce the cognitive complexity of traffic

situation. This complexity reduction results in airspace capacity improvement10,11. Current air traffic patterns in theU.S. contains highly structured routes that are favorable for the controllers. However current airspace sectorization

is not often in accordance with these structured routes and ATCs are not able to take full advantage of this existinghighly structured traffic. For example, an aircraft destined to ORD from LAX may cross up to 15 different sectors

while en route. Such a decentralized system produces significant amount of controller-to-controller and pilot-to-

controller coordination workload and this results in system inefficiency.

Recent advances in Air Traffic Management (ATM) technology are changing operating conditions of the ATC.

Today, with the use of advanced data links, one controller could be able to track an aircraft and communicate with apilot all the way from origin to destination. Advanced navigation equipment and data links such as Global

Positioning System (GPS), Airborne Separation Assurance System (ASAS), Automated Dependent Surveillance

Broadcasting (ADS-B) and Cockpit Display of Traffic Information (CDTI) enable pilots to provide separationassurance. Hence the ATC functions could become more strategic in nature.

B.

Lack of trained ATCs and excessive number of ARTCCsThe Federal Aviation Administration (FAA) currently employs approximately 15,272 controllers out of which,

more than 7,000, almost half the workforce, are expected to retire in the next nine years12. The FAA has proposed to

raise the retirement age to help deal with an unprecedented number of retirements. But this temporary solution doesnot address the issue in the long term. The retirement issue in addition to the increasing demand for air traffic

exacerbates challenges facing the ATM system. The Air Traffic facilities in continental U.S. are located in 20

ARTCCs across the country. As shown in Fig. 1, the overall traffic is not uniformly distributed among the Centers.

There are many administrative employees in each ARTCC other than the controllers. Such a decentralized systemresults in inefficiencies in terms of providing unnecessary infrastructure and staffing requirements. Reducing the

number of centers could result in significant savings. The FAA has initiated the National Airspace Redesign (NAR)

project, which in part aims for a more optimal sectorization by balancing the traffic load and sectors capacity13. The

NAR project also proposes a reduction in number of Centers. In this venue, a comprehensive methodology that

analyses the temporal and spatial distribution of airspace complexity and provides a scientific, yet practical,

technique for airspace sectorization is needed to guide the decision makers.


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C.

Deficiencies of previous research

The ATC workload is the major factor in designing the sector and center boundaries. The current heuristicapproaches for airspace design have reached the limit of their acceptability. To explore more automated and

systematic methodology, researchers have tackled the airspace partitioning problem in separate efforts. Variousmathematical methodologies like graph theory, genetic algorithm, computational geometry, and constraint

programming are applied to solve the portioning problem14-18. In general, these approaches do not consider

standalone metrics that reflect all the factors contributing to the ATC cognitive workload. Instead, they tried torepresent the workload by some simplified metrics that capture some of the contributing factors to the ATC

workload. In addition, to our knowledge, none of the proposed mathematical models has beenpractical enoughfor

designing the actualsector boundaries using realoperational data. The previous approaches take the existing sector

boundaries as a basis and try to optimize them locally. In other words, the workload has its meaning in the context ofexistingsector boundaries. The vertical movement of the aircraft is not usually considered and the proposed models

are representations of the airspace in 2-D.

II.

ATC Workload Modeling

Research in controller workload has been motivated by a desire to understand occupational stress, eliminate

operational errors, enhance safety, and improve controller training. Surprisingly there is no globally accepted

definition for ATC Controller workload controller workload is a confusing term and with a multitude of

definitions, its measurement is not uniform19. Workload measurement in ATC is often based on several parametersmeasured at the same time. As workload cannot be measured directly, it has to be inferred from quantifiable

variables. 19-35. Researchers have traditionally estimated workload through four basically different categories of

measures: Physical interaction of ATC with control devices like number of key strokes and communication tasks,

Aircraft Handled (000's), Jan-Dec 2003

2,975

2,959

2,852

2,805

2,713

2,595

2,274

2,228

2,182

2,131

2,053

2,041

2,021

2,005

1,780

1,701

1,684

1,601

1,461

1,272

0 500 1,000 1,500 2,000 2,500 3,000

ZOB

ZTL

ZAU

ZNY

ZID

ZDC

ZJX

ZME

ZMA

ZFW

ZKC

ZMP

ZAL

ZHU

ZBW

ZAB

ZDV

ZOA

ZLC

ZSE

Count, in thousands

Figure 1. Annual air traffic distribution among CON U.S. ARTCCs. Source:

FAA Factbook, March 2004. URL: http://www.atctraining.faa.gov/factbook.


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Physiological state of the ATC like heart rate and blood pressure,

Psychological state of the ATC as the amount of cognitive demand that is generated by traffic situations,

Traffic characteristics have been quantified through measurable constraints pertaining to the task and its

environment: total number of aircraft monitored during a work shift, number of coordination actions,

availability versus restriction of airspace, number of conflict points per hour, etc. Individually or combined,they are seen as indicators of controllers workload.

All of these metrics are measured during the actual operation or using real time simulations assuming that sector

boundaries are already designed. These measures have meaning in the context of already designed sectorboundaries. For the purpose of workload-based sectorization, the ATC workload needs to be modeled for any given

volume of airspace given a certain traffic pattern. In other words, when we are interested in designing the airspace,

there is no existing sector that conventional methods could be applied for workload measurement. Instead, a largescale simulation is essential to calculate variety of airspace metrics such as aircraft density, number and geometry of

conflicts, number of coordination actions, altitude changes, communication actions, etc. The simulation must be able

to calculate all the mentioned airspace metrics forgenericand uniform sector building-blocks.

Ref. 36 discuses an analytical method for workload modeling based on the traffic characteristics and sector

complexity. The ATC workload is divided into four variables:1- Horizontal Movement Workload (WLHM),

2- Conflict Detection and Resolution Workload (WLCDR),

3- Coordination Workload (WLC),4- Altitude-Change Workload (WLAC).

In each sector or group of sectors, the summation of these four variables gives the total workload, Eq.(1).

( , , , )TotalWL WLHM WLCDR WLC WLAC = (1)

The horizontal movement workload (WLHM) is determined by the number of aircraft in a sector (sector density)

and the average flight time. The Conflict Detection/Resolution (CDR) workload (WLCDR) is based on the conflictdetection using the type of conflict and the conflict severity. The coordination workload (WLC) is determined by the

type of coordination action including: voice call (coordination between two controlled airspace), clearance issue (i.e.

for changing the course), inter-facility transfer (coordination between two sectors from different ARTCCs), silent

transfer (coordination from controlled to uncontrolled airspace), intra-facility transfer (coordination between sectors

within an ARTCC), and tower transfer (coordination between Tower and TRACON ATC). The altitude-changeworkload (WLAC)is determined by the type of sector altitude clearance request for level-off, commence-climb and

commence-descent.The Total Airport and Airspace Modeler (TAAM) has been utilized in order to calculate the variables in Eq.(1).

TAAM is a large-scale fast-time ATM simulator that simulates the aircraft performance in all phases of flight (gate-to-gate), airport operations, and ATCs decision-making. TAAM counts and records different actions that controllers

take as well as the number of aircraft passing through each sector37. TAAM output tables are used to calculate eachof the four variable in Eq.(1). For detailed formulation and validation refer to Ref. 36.

III. Temporal and Spatial Distribution of ATC workload

A. Airspace partitioning

Todays airspace over continental U.S. is divided into low, high, and ultra-high altitude ranges that cover

controlled airspace in classes A, B, C, D, and E38. The operational environment of each altitude range is of different

nature. Most of the General Aviation (GA) aircraft use the low altitude airspace whereas commercial operations

take place in the high and ultra-high airspace depending on the flight range. Thus the traffic pattern in each altituderange has certain characteristics and for the purpose of airspace sectorization each altitude range should be treated

differently. Keeping this in mind, we partition the continental U.S. airspace into three layers as follows:

Mean Sea Level (MSL) to FL210, where short-hull turboprops tend to fly and Visual Flight Rule (VFR)operations take place.

FL210 to FL 310, where most of the short to medium-hull jet aircraft fly. It is also transition layer from

ultra-high jet routes to lower level airspace.

Above FL310, where en route airspace and jet routes are located.


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Each layer is further tiled to 2,566 hexagonal cells (hex-cells) which are assumed to be the finite elements of

airspace. Figure 2 illustrates a view of airspace partitioning process. In such a partitioning, we disregard any

existing sector or center boundary. We model the ATC workload for each hex-cell and describe how these cells

could be clustered to construct

sectors. The hex-cells need to besmall enough to provide reasonable

resolution also large enough to

capture conflict scenarios forcomputation of conflict

detection/resolution workload.

Current minimum lateral separationin en route airspace is 5 nm and

controllers often add a safety buffer

to this minimum. Taking this into

account, side of each hex-cell is

considered to be 24 nm or 0.4degree, which is enough to

accommodate 3 to 4 aircraft along

one route.Tiling a surface is possible by a

triangular, rectangular, orhexagonal mesh. For the purpose

of airspace sectorization the mostsuitable geometry seems to be a

hexagonal mesh. Computationally,

it is easier to cluster hex-cells in

every direction. Figure 3 illustrates

how hexagons can be clusteredtogether in different directions in a plane. For the triangular and

rectangular mesh, if we cluster two cells in diagonal directions,

they touch each other in their edges and do not have a commonside. So an aircraft cannot move from one cell to the other

without leaving the cluster. It is only in a hexagonal mesh that all

the cells have common sides for clustering in every direction.Also by using a hexagonal mesh, we avoid the acute and rightangles in triangle and rectangle that may result to short transit

times for aircraft passing close to the edges.

Our intention is to develop the methodology for a workload-

based airspace sectorization and we have selected the describedgeometry for airspace layers and hex-cell mesh as an initial

concept. One could divide the airspace to more than three layers

with different ranges or tile each layer with smaller/larger cells.

B. Simulation and hex-cell workload modeling

We use TAAM to simulate a one-day scenario of entire NAS operations. Each hex-cell is treated as a sector and

ATC workload is modeled using various airspace metrics that are calculated by TAAM. For each hex-cell the

coordination workload in Eq. (1) is set to zero (WLC=0) because, in reality, there is no hand in/off when an aircraftmoves form one hex-cell to the other. The required flight schedule and flight tracks are extracted from the Enhanced

Traffic Management System (ETMS) database and converted into proper format for TAAM. In the ETMS flight-table there are few sets of flying tracks recorded for each flight ID. ETMS updates the recorded routes every time

Airline Operation Centers (AOC) file a new flight plan. These updates are due to the FAA amendments and

advisories or to avoid inclement weather along the previously filed route. We filter the last filed route, before theaircraft push back, as an input to the simulation model. In the ETMS, there are many flights with missing attributes

like origin, destination, or departure/arrival time. Total number of flights that are retrieved from the ETMS is

roughly 45,000 flights. So we are missing 5,000-15,000 flights per day. Figure 4 shows a view of TAAM simulation

48 nm

41.5

7

nm

Over FL310

FL210 to FL 310

Below FL210

24 nm

48 nm

41.5

7

nm

Over FL310

FL210 to FL 310

Below FL210

24 nm

48 nm

41.5

7

nm

48 nm

41.5

7

nm

Over FL310

FL210 to FL 310

Below FL210

24 nm

Over FL310

FL210 to FL 310

Below FL210

24 nm

Figure 2. Airspace partitioning and the hex-cell structure.

RectangleHexagon TriangleClustering Direction RectangleHexagon TriangleClustering Direction

Figure 3. Comparison of different tiling

methods.


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with hex-cells as sectors and actual flown tracks. TAAM output tables provide all the parameters for calculation of

workload based on Eq. (1).

The hex-cell workload values

during 15 minute bins are plotted in

Fig.5. Each line represents one hex-cell and low and high altitude cells are

separated into two graphs. The low

altitude hex-cells generally havehigher workload due to their larger

altitude range. All the hex-cells follow

a same trend throughout the day andthere are few hex-cells with

exceptionally high workload values.

In the next sections we investigate the

geographical location of these cells.

Figure 6 categorizes the highaltitude hex-cells by their ARTCC for

each hour of the day. Each bar

represents one hex-cell and height ofthe bars indicates the total workload

during one hour intervals. The NewYork Center (ZNY), the smallest

Center in the NAS, contains the mostcomplex hex-cells whereas in larger

Centers like ZLC and ZMP there are

hex-cells with very low workload values. A comparison of Centers located in east and west coasts points out the

time lag between operational peaks in each side of the country. For instance, in ZLA, the peak workload starts at

15:00 Zulu whereas in ZDC, workload begins to grow at 11:00 Zulu.

Currently there are 20 ARTCCs that cover the whole continental NAS. The NAR project proposes a reductionfor number of ARTCCs. Reducing the number of Centers may potentially enhance the system efficiency in terms of

necessary infrastructure and staffing requirements. The methodology presented in this paper could be useful for

designing more efficient ARTCC boundaries. The total hourly workload for a Center is simply the integral of

workload values for all the cells. Figure 6 depicts the fact that current Center boundaries do not balance the airspace

complexity among all the Centers. Centers like ZLC, ZMP, and ZDV cover large areas of the NAS but they containvery small portion of overall traffic complexity. These low workload Centers could be expanded to cover larger

areas.

Figure 4. A view of TAAM simulation.

Figure 5. Workload trend of each hex-cell during one day for low and high altitude layers.


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C. Airspace Complexity Visualizer (ACV)

To explore the geographic location and daily workload trend for each hex-cell we have developed the Airspace

Complexity Visualizer (ACV). The ACV color codes the hex-cells based on their workload and displays a sequence

of 144 frames of entire NAS for 10 minute bins during the day. Figures 7 and 8 illustrate two frames of ACV forhigh and low altitude hex-cells during 18:10 to 18:20 Zulu. As we expect for the low altitude airspace, hex-cells

Figure 6. Workload values for high altitude hex-cells categorized by their ARTCCs.

Figure 7. One frame of ACV for time bin of 18:10 to 18:20 Zulu. Low altitude hex-cells are

color-coded based on their workload values.


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with high workload are located in vicinity of large airports and densely population areas whereas in the high altitude

airspace the complex airspace is further out the airports in the en route airspace.

Unfortunately it is not possible to include more frames of ACV in this paper. Running the ACV for the entireday displays how the airspace complexity propagates throughout the NAS. Congested areas grow in a very

structured fashion between airports and the routing structure is clearly identifiable.

IV. Airspace Sectorization

In this section we discuss an optimization-based methodology for clustering the hex-cells and construct sectors.

A.Requirements for an optimum airspace secotrization

We identify the top-level requirements for an efficient sectorization system as follows:

The system shall;

1. be bounded by the Canadian & Mexican borders as well as the boundaries between oceanic airspace

and current ARTCCs,

2. be developed independent from the inland ARTCC and sector boundaries,3. be implemented in accordance to the operational flight levels,

4. focus on the en route airspace. The Terminal Radar Approach Control (TRACON) areas shall not be

included in the system,5. minimize the overall coordination workload,

6. balance the spatial distribution of overall workload among all the sectors,

7.

provide reasonable average sector transit time and avoid very short sector transit times,8. avoid highly concave sectors.

Requirements 1 to 3 are already considered in the process and we focus on the rest of the requirements. The

operational environment in the TRACON area is different from the en route airspace39. The arrival/departure aircraft

entering the TRACON are assigned Standard Terminal Arrival Routes (STAR), Standard Instrument Departure

(SID) routes, and pre-defined holding patterns. In the TRACON, the minimum lateral separation is 3 nm versus 5

nm in the en route. The main task of TRACON controllers is sequencing assignment which is assigned based on therunway configuration, the structure of SIDs and STARs, and wake vortex separation standards. As a result, local

considerations are necessary for TRACON sectorization. In this paper we focus on sector design out of the

TRACON areas. The minimization of coordination workload is one of the main objectives in our methodology.

Figure 8. One frame of ACV for time bin of 18:10 to 18:20 Zulu. High altitude hex-cells are

color-coded based on their workload values.


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Coordination actions include controller-to-controller and controller-to-pilot communications for hand-off/hand-in

and frequency assignments. This objective is satisfied if we minimize the hand-off/hand-in by decreasing the

number of sectors. By balancing the distribution of workload among the sectors, we eliminate sectors with very high

complexity as well as low complex sectors. This removes the airspace chokepoints which are one of the main

sources of airspace inefficiencies. From the human perception point of view, it is important that aircraft remain inthe sectors for long enough periods. Short transit times do not allow the controllers to comprehend the traffic

situation and take necessary coordination actions. Short transit times typically occur in highly concave sectors where

aircraft cross the sector close to the edges. Thus maintaining convex shapes for sectors is set as a requirement.

B. Sectorization Algorithm

1. Defining a design periodWe model the workload as a varying

function of time. Any clustering algorithm

produces different sector boundaries for eachperiod of the day. But human factor studies

suggest a constant sectorization allowing the

ATCs to sketch the traffic patterns in their

mind10,11,&40

. The ATCs memorize the enter/exitpoints and they often know at what time which

traffic is entering their sector, where are the

potential conflicting areas, and what are thenecessary resolution actions. They develop

abstractmental models of the traffic pattern. Ifwe change the sector boundaries dynamically

throughout the day, ATCs will not be able to

develop such abstract models. This decreases thesituational awareness and imposes high

operational stress on the ATCs. Therefore we

define a representative design-period thatcaptures the workload dynamics throughout the

day. In Fig. 9, total workload for each center is

calculated by integrating the workload values for

all hex-cells within each ARTCC. Each line

represents the percentage of maximum dailyworkload for each center during different time bins. It

can be observed that at time 21:00 Zulu all the centers

are operating above 80 percent of their maximum dailyworkload. It means that despite the time lag for

operational peaks, at 21:00 Zulu most of the high

altitude airspace is very congested. As an initial phase,

we select this time as the design-period and applyclustering algorithms based on the hex-cells workload

during 20:00 to 21:00 Zulu. Future research may

suggest other methods for defining this design-period to

capture the systems dynamics more rigorously.

2. Geometry of the clustering algorithm

So far, we have 2,566 hex-cells that need to beclustered into n sectors. We define a set of potential

centers for sectors on top of the hex-cell mesh. It meansthat the clusters start to grow from these potential

centers. The geometry of centers for potential sectors is

illustrated in Fig. 10. Parameter S denotes the side ofthe hex-cells which is set to 24 nm.

The number of potential sectors is large enough that

it does not restrict the clustering process. In other words, the clustering algorithm has enough flexibility to open

sectors and assign hex-cells to achieve the optimum solution.

Figure 9. Percentile of high altitude workload for each

ARTCC in one hour increments. At time 21 Zulu all the

centers are operated with over 80 percent of their maximum

daily workload.

)S32(

. ...

S

. .

.. .

.

.1.5S

.

..

..

.. . .

3S

S3

3S

6S

Center for

potential sector

)S32(

. ...

S

. .

.. .

.

.1.5S

.

..

..

.. . .

3S

S3

3S

6S

Center for

potential sector

Figure 10. The geometry of clustering algorithm.

Potential centers for sectors are shown in red circles.

The side of each hex-cell isS=24 nm.


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3. Clustering algorithm

One can think of the clustering

problem as a standard facility location

problem, where we have a set of

customers that need to be assigned tofacilities. Sectors are assumed to be

the facilities and the customers are the

hex-cells. Not all the facilities have tobe opened so as for the sectors. For

the entire NAS, we create 649

potential centers for sectors. We alsofilter out the hex-cells with zero

workload during the design period.

These zero-workload hex-cells do not

have any impact in the clustering

algorithm and they can be assigned toany sector after the clustering is

finished. At the end, we have 2,031

customers and 649 potential facilitiesas shown in Fig.11. For visualization

purposes from this point on, we represent the hex-cells bytheir center points. The facility location problems are

extensively studied by operation researchers41and there isa wealth of knowledge in this area. However constraints

for avoiding concavity or sector contiguity are not

necessary in general facility location problems. We

develop a linear integer minimization program to solve the

clustering problem. The algorithm is summarized in Table1.

The objective is to minimize the variation of workload

among sectors. In other words, we cluster the hex-cells into sectors in such a way that balances the distribution ofworkload among the sectors. The detailed mathematical formulation of minimization problem is a long discussion

and beyond the scope of this paper.

4.

Clustering exampleOur intention is to apply the clustering algorithm

for the entire NAS at the same time. But, as an initial

step, we select the high altitude layer in Chicago

Center (ZAU) to test the algorithm. The centers for

hex-cells and potential sectors for ZAU high altitudelayer are illustrated in Fig. 12. There are 70 hex-cells

and 16 potential sectors. So the minimization

algorithm needs to solve (70 16) 1,120 = combinatorial

variables to assign the hex-cells to sectors. The

maximum number of sectors to be opened is a givenparameter to the minimization problem. In the case of

ZAU we assign the maximum number of sectors to 6.

So 70 hex-cells will be assigned to maximum 6opened sectors. The minimization problem is solved

using CPLEX solver and the results are shown in Fig.13. As illustrated in this figure, 6 sectors are opened

and they are all convex and continuous. However one

needs to pay attention that the ZAU center boundariesdo not form a convex polygon. In Fig. 13, the indented sector sides are due to the concave shape of the ZAU Center

itself.

Figure 11. Potential centers for sectors are shown in blue and centers

for non-zero workload hex-cells are shown in red.

n(cell)=70

n(sector)=16

n(cell)=70

n(sector)=16

Figure 12. Center-points of potential sectors and center-

points of hex-cells in high altitude layer of ZAU center.

MINIMIZE (variation of workload among sectors)

SUBJECT TO: sector contiguity

avoiding highly concave sectors

number of sectors is limited

avoid extremely large sectors

some other ordinary constraints

Table 1. Summary of minimization problem.


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5. Problem complexity

In the ZAU example there are (16 70) 1,120 =

combinatorial variables to be solved. The CPLEX run-

time in a Pentium-M 1.6 GHz processor, with 1 GB

RAM was less than a minute. But the complexity of

problem increases non-linearly w.r.t the number of

hex-cells and sectors. For each altitude layer of entireNAS we have (649 2031) 1, 318, 119 = variables. This

is an extremely large scale optimization problem. We

are currently working on the efficiency of the

algorithm. Another approach could be to reduce theproblem size by dividing the NAS into East-WestMississippi or Atlantic-Pacific segments, or splitting

the NAS using the time-zones. Then apply the

clustering algorithm for a smaller population of hex-

cells and sectors.

D. An alternative approach; workload as a continuous function of time, latitude, and longitude

As explained before, the hex-cells have to be large enough to capture the conflicting scenarios. This eliminates

the resolution of hex-cell mesh. To achieve higher resolution, we linearly interpolate the workload values between

centers of the hex-cells. For each time bin, the linear interpolation yields a continuous workload surface which is afunction of time, latitude, and longitude, Eq. (2).

tWL = f(lat,lon)

where :

f is a generic function

t denotes the time interval

(2)

The workload function is indexed by time intervals, for example WL1440denotes the workload function during

14:30 to 14:40 Zulu. Figure 14 illustrates the projection of a workload surface into a plain for time interval of 14:30

to 14:40 Zulu (WL1440). The ACV also animates these surfaces and visualizes the propagation of airspace complexity

throughout the NAS continuously. The existing jet routes between congested airports are clearly identified and it ispossible to study the evolution of high workload areas throughout the day.

We also calculate iso-workload contours for each WLt. These contours are shown in Fig. 15. The partial

derivative of WLt, w.r.t latitude and longitude yields the gradient vector 1440 WL . The gradient vectors are

perpendicular to the iso-workload contours and their length indicates the magnitude of the gradient, Eq. (3).

1440

WL WL

WL i jlat lon

= + (3)

For our next approach, we will make an analogy with the world of physics and crystal growing. To grow acrystal, one begins by heating the raw materials to a liquid state. This molten material is then slowly cooled, until the

crystal structure is frozen in. If the temperature is decreased too quickly, flaws in the crystal can be locked in. Slow

temperature decrease allows these flaws to work themselves outforming a much better crystal. This process is called

annealing.

ZAUZAU

Figure 13. Sectorization of high altitude airspace in

ZAU Center. Maximum number of opened sectors is

assigned to 6.


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One can think of the final state of a crystal as a local

optimum: no small movement of the molecules can decrease

the total energy content. A perfect crystal contains theminimum energy content of all the final possibilities.

Because molecules only move locally, the laws of physics

only require that some local optimum be found. But if

annealing creates better solutions, perhaps we can simulatethis annealing process.

We propose that the sectorization could be modeled as anannealing process to calculate the global optimum in terms ofATC workload distribution. By constructing continuous

functions for workload, we transform the problem domain so

that we can apply Simulated Annealing (SA) techniques for

the sectorization process. The discussion of sectorization by

SA is beyond the scope of this paper and we leave thismethodology for the future work.

V. Conclusion

An ATC workload-based methodology is discussed to solve the airspace sectorization problem. ATC workload

is modeled using large scale simulation for elements of airspace regardless of current sector and center boundaries.Hexagonal cells are assumed to be the building blocks of sectors and these building blocks are clustered to construct

sectors. Initial results for sectorizarion of a single ARTCC is promising. We are currently working on efficiency ofthe clustering algorithm and applying the methodology for the entire NAS. We define the design-period as the time

period that most of the NAS is congested. To include the impact of weather related disruptions, it is possible to

simulate the workload for few bad-weather days and define the design period for combination of different days

including when the inclement weather interrupts the operations. We use TAAM to calculate the required airspace

metrics for workload modeling. The presented methodology is general and other ATM models could be used forworkload measurement and validation of TAAM outputs.

Figure 14. Planar Projection of the high altitude WL1440 surface. Large airports and center

boundaries are illustrated in magenta and red.

Figure 15. Iso-workload contours and gradient

vectors of WL1440for the high altitude layer.


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As an alternative approach we model the workload as a continuous function of time, latitude, and longitude of

each point in the NAS. Accordingly we propose to use Simulated Annealing techniques for designing the sector

boundaries. This could open new venues for development of alternate clustering algorithms.

The presented methodology for analysis of tempo-spatial distribution of ATC workload could also be used to

determine the optimum number and location of ARTCCs.

AcknowledgmentsThis work was supported by the FAA aviation research grant 00-G-016 and by grant NAG-2-1643 from the

NASA. Special thanks to Karla Hoffman (GMU), John Shortle (GMU), Lance Sherry (GMU), Chun-Hung Chen(GMU), Terry Thompson (Metron Aviation Inc.), and Mark Klopfenstein (Metron Aviation Inc.) for technical

suggestions. Also thank to Ariela Sofer (GMU), Lauren Magruder (GMU), Colleen Peranteau (FAA), Steve

Bradford (FAA), and Barri Caldwell (NASA) for their support.

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